Is it possible to become a Brahmajnani(A Knower of God) by following the path of discrimination according to the Vedanta philosophy?
Yes, one may reach Him [God] by following the path of discrimination too: that is called Jnanayoga. But it is an extremely difficult path. I have told you already of the seven planes of consciousness. On reaching the seventh plane the mind goes into samadhi. If a man acquires the firm knowledge that Brahman alone is real and the world illusory, then his mind merges in samadhi.
But in the Kaliyuga the life of a man depends entirely on food. How can he have the consciousness that Brahman alone is real and the world illusory? In the Kaliyuga it is difficult to have the feeling, 'I am not the body, I am not the mind, I am not the twenty-four cosmic principles; I am beyond pleasure and pain, I am above disease and grief, old age and death.' However you may reason and argue, the feeling that the body is identical with the soul will somehow crop up from an unexpected quarter. You may cut a peepal-tree to the ground and think it is dead to its very root, but the next morning you will find a new sprout shooting up from the dead stump.
One cannot get rid of this identification with the body; therefore the path of bhakti is best for the people of the Kaliyuga. It is an easy path.
Reference: The Gospel of Sri Ramakrishna (7.1 The Master And Vijay Goswami)